Collective fixed points and a system of coincidence theorems in product FCFC-spaces and applications

By using a continuous selection theorem, some new collective fixed point theorems and coincidence theorems for the families of set-valued mappings defined on the product space of noncompact FCFC-spaces are proved under very weak assumptions. As applications, some nonempty intersection theorems, inclusion theorems and existence theorems of solutions for systems of inequalities are established in the product space of noncompact FCFC-spaces. These results generalize many known results from the recent literature.